We propose a new phase-field model formulated within the system of lattice Boltzmann (LB) equation for simulating solidification and dendritic growth with fully coupled melt flow and thermosolutal convection–diffusion. With the evolution of the phase field and the transport phenomena all modeled and integrated within the same LB framework, this method preserves and combines the intrinsic advantages of the phase-field method (PFM) and the lattice Boltzmann method (LBM). Particularly, the present PFM/LBM model has several improved features compared to the existing phase-field models including: (1) a novel multiple-relaxation-time (MRT) LB scheme for the phase-field evolution is proposed to effectively model solidification coupled with melt flow and thermosolutal convection–diffusion with improved numerical stability and accuracy, (2) convenient diffuse interface treatments are implemented for the melt flow and thermosolutal transport which can be applied to the entire domain without tracking the interface, and (3) the evolution of the phase field, flow, concentration, and temperature fields on the level of microscopic distribution functions in the LB schemes is decoupled with a multiple-time-scaling strategy (despite their full physical coupling), thus solidification at high Lewis numbers (ratios of the liquid thermal to solutal diffusivities) can be conveniently modeled. The applicability and accuracy of the present PFM/LBM model are verified with four numerical tests including isothermal, iso-solutal and thermosolutal convection–diffusion problems, where excellent agreement in terms of phase-field and thermosolutal distributions and dendritic tip growth velocity and radius with those reported in the literature is demonstrated. The proposed PFM/LBM model can be an attractive and powerful tool for large-scale dendritic growth simulations given the high scalability of the LBM.

我们提出了一种在晶格 Boltzmann (LB) 方程系统内制定的新相场模型，用于模拟凝固和枝晶生长与完全耦合的熔体流动和热溶对流 - 扩散。随着相场的演变和传输现象都在同一 LB 框架内建模和集成，该方法保留并结合了相场法 (PFM) 和格子玻尔兹曼法的内在优势(LBM)。特别是，与现有的相场模型相比，目前的 PFM/LBM 模型具有几个改进的特征，包括：（1）提出了一种用于相场演化的新型多松弛时间（MRT）LB 方案，以有效地模拟凝固耦合具有熔体流动和热溶质对流 - 扩散具有更高的数值稳定性和准确性，(2) 对熔体流动和热溶质输运实施了方便的扩散界面处理，可以应用于整个域，而无需跟踪界面，以及 (3) 演化LB 方案中微观分布函数水平上的相场、流动、浓度和温度场的分离与多时间缩放策略（尽管它们完全物理耦合），因此，可以方便地模拟高路易斯数（液体热扩散率与溶质扩散率之比）下的凝固。本 PFM/LBM 模型的适用性和准确性通过包括等温在内的四项数值试验得到验证，等溶质和热溶质对流 - 扩散问题，证明了在相场和热溶质分布以及树枝状尖端生长速度和半径方面与文献中报道的非常吻合。鉴于 LBM 的高可扩展性，所提出的 PFM / LBM 模型可以成为大规模树突生长模拟的有吸引力且强大的工具。